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(C) The ratio of specific heat at constant pressure to specific heat at constant volume is given by the adiabatic index $\gamma = C_p / C_v$.For a pol

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$1.28$

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(C) The ratio of specific heat at constant pressure to specific heat at constant volume is given by the adiabatic index $\gamma = C_p / C_v$.For a polyatomic gas like $NH_3$ (ammonia),which has non-linear molecules,the degrees of freedom $f = 6$.The adiabatic index is calculated as $\gamma = 1 + (2/f)$.Substituting $f = 6$,we get $\gamma = 1 + (2/6) = 1 + 0.33 = 1.33$.However,for real polyatomic gases,the vibrational degrees of freedom contribute,making $\gamma$ typically lower than the ideal value of $1.33$.Among the given options,$1.28$ is the most accurate value for $NH_3$ at room temperature.

Find the ratio of specific heat at constant pressure $(C_p)$ to the specific heat at constant volume $(C_v)$ for $NH_3$.

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